You want to sell your car having only done 1700 miles, you are going to lose alot of money no question.
Why dont you get a mortgage for the value of the house and add the extra needed to clear the debt of your car.
Consolidate your debts so you dont have to sell and lose money, keep the car and get the house. You will probably need something decent to use for transport for work.( Im guessing )
have you thought about taken out a loan for a longer term that will lower the monthly payments so you can afford the mortgage you want.
( these are excuses you can put to your wife/girlfriend if she is putting pressure on you to sell
)